upper bound vs lower bound

Both 'upper bound' and 'lower bound' are correct phrases used in mathematics, statistics, and other fields to refer to the maximum and minimum limits of a range, respectively. They are commonly used in various contexts to describe constraints, limits, or thresholds.

Last updated: March 22, 2024 • 661 views

This phrase is correct and commonly used in mathematics, statistics, and other fields to refer to the maximum limit of a range.

"upper bound "

The 'upper bound' refers to the maximum limit or value in a given range or set of data.

Examples:

The upper bound of the data set is 100.
We need to determine the upper bound for the variable in the equation.
What is the upper bound for the number of participants in the study?

Show examples from the web [+]

This level should normally be set above the upper bound referred to in paragraph 27 for Tier 1 capital instruments.
This level should normally be set above the upper bound referred to in paragraph 27 for Tier 1 capital instruments [24].
(including the upper bound to the impact of the guarantee)
In all cases, even incorporating all the possible effects of the guarantee in dealings with customers and suppliers, the upper bound to the intensity of the aid remains well within the maximum permissible.
500 pg I-TEQ/kg (upper bound detection limit)
Of the 806 infusions administered in patients enrolled in both studies 10.8% (1-sided 95% CI upper bound = 12.9%) were associated with an adverse event suspected to be related to the product.
That comparator set shows a median ROS of 7,4 % for the period 1998-2007 and a third-quartile ROS of 12 % as upper bound for reasonable profit.
The value u2σ is the upper bound of the 2σ confidence interval of the maximum resultant induced air speeds in the x-y platform plane.
The average upper bound is 11,7 % and the average lower bound is 6,1 %.
Compared with the December 2006 Eurosystem staff projections, the upper bound of the range projected for inflation in 2007 is somewhat lower, largely reflecting the fall in oil prices.
The value Δp2σ shall be the upper bound of a 2σ interval of (pmax - pmin) based on at least 10 independent and comparable test samples (at a certain measuring height) with ambient wind speeds of less than or equal to 2 m/s.
In the ECB staff macroeconomic projections of March 2007, the upper bound of the range projected for inflation in 2007 was somewhat lower than in the Eurosystem staff projections of December 2006, largely reflecting the significant decline in oil prices.
Upper bound [215](insurance premium)
Upper bound to the impact of the guarantee in dealings between IFP and its suppliers
CI = confidence interval, OS = overall survival time, a '+ 'denotes that the upper bound limit had not been reached at cut-off
Concerning the return on assets, the WIK study shows a median ROA of 7,33 % and an upper bound of 13,41 %.
Given the information at the Commission's disposal, one can therefore consider that the expected cash flows presented in the 2004 business plan represented an upper bound [31].
Therefore the Commission considers that a maximum rate of 5 % of the turnover generated by the service covered is in any case an upper bound to the premium which would be necessary to cover such a risk.
However, the WIK study not only presents the median return but also an upper bound for the reasonable profit, e.g. the third quartile of the comparable competitors' profit which amounts to a ROS of 6,77 %.
[10] For this estimate the intermediate bound was taken for contamination, while the upper bound was taken for the other threats, see section 2.6.2 in the impact assessment. -

Alternatives:

maximum limit
ceiling value
top limit
maximum boundary
maximum threshold

This phrase is correct and commonly used in mathematics, statistics, and other fields to refer to the minimum limit of a range.

"lower bound "

The 'lower bound' refers to the minimum limit or value in a given range or set of data.

Examples:

The lower bound of the data set is 20.
We need to establish the lower bound for the variable in the equation.
What is the lower bound for the acceptable range of values?

Show examples from the web [+]

Value indicating the lower bound of the height/depth range.
Value indicating the lower bound of the calorific range.
Thus, the lower bound of the expected return on equity for a private investor would be:
We consider the lower bound of this interval for our estimation of the market risk premium. Rm
The lower bound problem stems from the fact that a central bank cannot force nominal interest rates to levels below zero.
A lower bound greater than - 15% demonstrates non-inferiority between Aloxi and comparator. c Chi-square test.
I figured out how to get a lower bound for L,
As the lower bound of the MTO range is equal to the minimum benchmark (estimated at a deficit of around 1 % of GDP), achieving the MTO should fulfil the aim of providing a safety margin against the occurrence of an excessive deficit.
An important topic that was analysed in two studies was the zero lower bound on nominal interest rates and the risks of prolonged deflation or a deflationary spiral.
This new lower bound of exemption contributes to SME's brisker economic performance and by the way resulting in much higher level of employment in the entire territory of EU, coinciding with Lisbon's Goals.
Once again, I'm the lower bound.
This new lower bound of exemption contributes to SME's brisker economic performance, generating more employment across the EU, further realising the Lisbon objectives.
As regards the sum of the four substances (PAH4), lower bound concentrations should be used as the basis for compliance decisions.
The average upper bound is 11,7 % and the average lower bound is 6,1 %.
For their macroeconomic calculations, Member States are required to use as a minimum lower bound the projected ETS carbon prices in the Commission reference scenario up to 2050, assuming implementation of existing legislation, but not decarbonisation (first line of table below).
The Commission took a conservative approach in the estimation of the market risk premium and considered the lower bound of this interval, namely 6,8 %.
Based on the data of both comparable sets, the Deloitte-II study recommends a range from a lower bound ROS of 6,1 % up to an upper bound ROS of 11,7 % as benchmark for a reasonable profit.
The difference between upperbound level and lower bound level must not exceed 20 % for feed with a dioxin contamination in the range or above the maximum level.
The difference between upperbound level and lower bound level shall not exceed 20 % for foodstuffs with a dioxin contamination of about 1 pg WHO-TEQ/g fat (based on the sum of PCDD/PCDF and dioxin-like PCBs).
The difference between upper-bound level and lower bound level shall not exceed 20 % for foodstuffs with a contamination of about 1 pg WHO-TEQ/g fat (based on the sum of PCDD/Fs and dioxin-like PCBs).

Alternatives:

minimum limit
floor value
bottom limit
minimum boundary
minimum threshold

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upper bound vs lower bound

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